billy puts $800.00 into an account to use for school expenses. the account earns 14% interest, compounded…

billy puts $800.00 into an account to use for school expenses. the account earns 14% interest, compounded continuously. how much will be in the account after 6 years? use the formula $a = pe^{rt}$, where $a$ is the balance (final amount), $p$ is the principal (starting amount), $e$ is the base of natural logarithms ($\\approx2.71828$), $r$ is the interest rate expressed as a decimal, and $t$ is the time in years. round your answer to the nearest cent.

billy puts $800.00 into an account to use for school expenses. the account earns 14% interest, compounded continuously. how much will be in the account after 6 years? use the formula $a = pe^{rt}$, where $a$ is the balance (final amount), $p$ is the principal (starting amount), $e$ is the base of natural logarithms ($\\approx2.71828$), $r$ is the interest rate expressed as a decimal, and $t$ is the time in years. round your answer to the nearest cent.

Answer

Explanation:

Step1: Identify the values of P, r, and t

$P = 800$, $r=0.14$, $t = 6$

Step2: Substitute values into the formula

$A=Pe^{rt}=800\times e^{0.14\times6}$

Step3: Calculate the exponent

$0.14\times6 = 0.84$

Step4: Find the value of $e^{0.84}$

$e^{0.84}\approx2.316367$

Step5: Calculate the final amount A

$A = 800\times2.316367=1853.0936$

Answer:

$$1853.09$